//  File MIT-Lab-18-06-04-05.txt.  Edition 5/15/2012.

// Title
Explantory_Variable/Error_Term_Correlation

//  Omitted Variables or Measurement Error
      ExplErrCorr

//  List for Y on X Constant, Coefficient, and Error Term Variance
      10 30 10 10
      -2.0 2.0 2.0 2.0
      -5.0 5.0 5.0 5.0
      100  500  200  300

// List Sample Size
      50 500 25 50
      
// Correlation Coefficients: X1Z, X2Z, and X1X2
      .50  .75  .25  .50
      .00  .10  .10  .00
     -.30  .60  .30  .30

// Correlation Coefficient Betas
//   The order is X1Z X2Z X1X2
    .493 .000 -.296    .721 .000 -.289    .549 .091 -.363    .827 .091 -.398
    .366 .000  .000    .532 .000  .000    .383 .091 -.038    .568 .091 -.057
    .311 .000  .186    .457 .000  .183    .305 .091  .162    .461 .091  .145
    .290 .000  .348    .459 .000  .367    .267 .091  .333    .429 .091  .326


// Measurement Error X1Z Correlation Betas
    .500 .662
// Measurement Error Variance
     1.0 3.0 1.0 2.0
     
// Data Check: Needed to account for violatile IV behavior
// Simulation ignores repetition in which the estimate differs
// from the actual value by more than the Data Check value.
    25

//  Problem Specs: abcd Corr[X1,Z] Corr[X2,Z] Corr[X1,X2] Coef1Value Coef2Value SampleSize
//   abcd
//   a: Pause checkbox
//   b: Both 0-Both Xs    1-Only X1
//   c: Parameter to estimate. 0, 1, or 2: 0-Constant  1-X1  2-X2
//   d: Estimation procedure. 0-OLS 1-IV


` 0010 .00 .00 .00 2 5 50
Objective: Illustrate that the OLS estimation procedure is unbaised and consistent
 when the standard ordinary least squares (OLS) premises are satisfied.
_
Note that the explanatory and the error term are independent; their
 correlation coefficient (Corr X&E) equals .00.

` 0010 .00 .00 .00 2 5 50
1. Initially, the sample size is specified as 50. 
 Click the Start button and after many, many repetitions click the Stop button.
_
1a. What does the mean of the coefficient estimates equal?
_
1b. What does the variance of the coefficient estimates equal?


` 0010 .00 .00 .00 2 5 100
2. Next, note that the sample size has been increased from 50 to 100.
_
2a. What does the mean of the coefficient estimates equal?
_
2b. What does the variance of the coefficient estimates equal?



` 0010 -.00 .00 .00 2 5 150
3. Now, note that the sample size has been increased from 100 to 150.
_
3a. What does the mean of the coefficient estimates equal?
_
3b. What does the variance of the coefficient estimates equal?


` 0010 -.00 .00 .00 2 5 400
4. Now, note that the sample size has been increased from 100 to 150.
_
4a. What does the mean of the coefficient estimates equal?
_
4b. What does the variance of the coefficient estimates equal?